The Full Laplace-Beltrami operator on U(N) and SU(N)

1999/01/08 by Ole L. Trinhammer, O. L. Trinhammer, Trinhammer, O. L. +3
Computer Science · Mathematics · Physics and Astronomy · #22E70 #43A90 #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math-ph #math.MP #msc:22E70 #msc:43A90

paper · pdf · doi:10.48550/arxiv.math-ph/9901002

11 pages, 1 figure

openalex publication_date 1999/01/08 · arxiv created 2012/04/10 · arxiv updated 2012/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Laplacian on the Lie groups U(N) and SU(N) is given in a parametrized edition for practical purposes. The radial part is often seen in work on lattice gauge theory, but here is derived also the off-diagonal part which in SU(3) and U(3) is expressed via the well known Gell-Mann matrices but with a more easily memorized notation. Relations to I, U and V spin are also shown.

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